Face numbers of centrally symmetric polytopes from split graphs

Face numbers of centrally symmetric polytopes from split graphs

Ragnar Freij, Matthias Henze, Moritz W. Schmitt, Günter M. Ziegler – 2012

Focus Area 1: High-complexity Geometry
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3^d-conjecture for such polytopes (they all have at least 3^d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3^d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.

Title

Face numbers of centrally symmetric polytopes from split graphs

Author

Ragnar Freij, Matthias Henze, Moritz W. Schmitt, Günter M. Ziegler